In what scenarios would the dispatcher recalculate the flight plan and send it to the pilot via ACARS after take-off?
Anytime the original routing or altitude is significantly changed, a new flight plan is calculated by dispatch and sent to the aircraft. Significant changes could mean the aircraft may not have enough fuel to reach the destination. Even minor changes are routinely re-calculated and sent to the aircraft.
The pilots send dispatch the new routing and altitude along with an updated ETA and FOB(fuel onboard) for the next waypoint. The flight plan is then recalculated from that point and sent to the aircraft.
Routing changes can be due to traffic conflicts, airspace closures, military activity, volcanic activity, etc.
If for any reason the aircraft is unable to contact dispatch, the pilots must do their own calculations to insure they have enough fuel.
If the fuel remaining is marginal, the flight can be re-filed with a new alternate closer to the final destination. If conditions can be met, the flight might be re-filed with "no alternate".